Multidimensional signal, image, and video processing and coding

Digital images have become mainstream of late notably within HDTV, cell phones, personal cameras, and many medical applications. The processing of digital images and video includes adjusting illumination, manufacturing enlargements/reductions, and creating contrast. This development has made it possible to take long forgotten, badly damaged photos and make them new again with image estimation. It can also help snapshot photographers with image restoration, a method of reducing the influence of an unsteady hand.

Dr. Woods has constructed a book for professionals and graduate students that will give them the thorough understanding of image and video processing that they need in order to contribute to this hot technology's future advances. Examples and problems at the end of each chapter help the reader digest what has just been read. Forged from a theoretical base, this exceptional book develops into an essential guide to hands-on endeavors in signal processing.

Preface	p. xiii
Acknowledgments	p. xvii
1 Two-Dimensional Signals and Systems	p. 1
1.1 Two-Dimensional Signals	p. 2
1.1.1 Separable Signals	p. 6
1.1.2 Periodic signals	p. 7
1.1.3 2-D Discrete-Space Systems	p. 9
1.1.4 Two-Dimensional Convolution	p. 11
1.1.5 Stability of 2-D Systems	p. 13
1.2 2-D Discrete-Space Fourier Transform	p. 14
1.2.1 Inverse 2-D Fourier Transform	p. 18
1.2.2 Fourier Transform of 2-D or Spatial Convolution	p. 19
1.2.3 Symmetry Properties of Fourier Transform	p. 26
1.2.4 Continuous-Space Fourier Transform	p. 28
1.3 Conclusions	p. 31
1.4 Problems	p. 31
References	p. 33
2 Sampling in Two Dimensions	p. 35
2.1 Sampling Theorem-Rectangular Case	p. 36
2.1.1 Reconstruction Formula	p. 40
2.1.2 Ideal Rectangular Sampling	p. 43
2.2 Sampling Theorem-General Regular Case	p. 48
2.2.1 Hexagonal Reconstruction Formula	p. 52
2.3 Change of Sample Rate	p. 57
2.3.1 Downsampling by Integers M[subscript 1] x M[subscript 2]	p. 57
2.3.2 Ideal Decimation	p. 58
2.3.3 Upsampling by Integers L[subscript 1] x L[subscript 2]	p. 61
2.3.4 Ideal Interpolation	p. 62
2.4 Sample-Rate Change-General Case	p. 64
2.4.1 General Downsampling	p. 64
2.5 Conclusions	p. 66
2.6 Problems	p. 66
References	p. 70
3 Two-Dimensional Systems and Z-Transforms	p. 71
3.1 Linear Spatial or 2-D Systems	p. 72
3.2 Z-Transforms	p. 76
3.3 Regions of Convergence	p. 79
3.3.1 More General Case	p. 82
3.4 Some Z-Transform Properties	p. 83
3.4.1 Linear Mapping of Variables	p. 84
3.4.2 Inverse Z-Transform	p. 85
3.5 2-D Filter Stability	p. 89
3.5.1 First-Quadrant Support	p. 91
3.5.2 Second-Quadrant Support	p. 91
3.5.3 Root Maps	p. 96
3.5.4 Stability Criteria for NSHP Support Filters	p. 98
3.6 Conclusions	p. 100
3.7 Problems	p. 101
References	p. 103
4 Two-Dimensional Discrete Transforms	p. 105
4.1 Discrete Fourier Series	p. 106
4.1.1 Properties of the DFS Transform	p. 109
4.1.2 Periodic Convolution	p. 111
4.1.3 Shifting or Delay Property	p. 112
4.2 Discrete Fourier Transform	p. 113
4.2.1 DFT Properties	p. 115
4.2.2 Relation of DFT to Fourier Transform	p. 120
4.2.3 Effect of Sampling in Frequency	p. 121
4.2.4 Interpolating the DFT	p. 122
4.3 2-D Discrete Cosine Transform	p. 123
4.3.1 Review of 1-D DCT	p. 125
4.3.2 Some 1-D DCT Properties	p. 128
4.3.3 Symmetric Extension in 2-D DCT	p. 131
4.4 Subband/Wavelet Transform (SWT)	p. 132
4.4.1 Ideal Filter Case	p. 132
4.4.2 1-D SWT with Finite-Order Filter	p. 135
4.4.3 2-D SWT with FIR Filters	p. 137
4.4.4 Relation of SWT to DCT	p. 138
4.4.5 Relation of SWT to Wavelets	p. 138
4.5 Fast Transform Algorithms	p. 140
4.5.1 Fast DFT Algorithm	p. 140
4.5.2 Fast DCT Methods	p. 141
4.6 Sectioned Convolution Methods	p. 142
4.7 Conclusions	p. 143
4.8 Problems	p. 144
References	p. 147
5 Two-Dimensional Filter Design	p. 149
5.1 FIR Filter Design	p. 150
5.1.1 FIR Window Function Design	p. 150
5.1.2 Design by Transformation of 1-D Filter	p. 156
5.1.3 Projection-Onto-Convex-Sets Method	p. 161
5.2 IIR Filter Design	p. 165
5.2.1 2-D Recursive Filter Design	p. 165
5.2.2 Fully Recursive Filter Design	p. 171
5.3 Subband/Wavelet Filter Design	p. 174
5.3.1 Wavelet (Biorthogonal) Filter Design Method	p. 178
5.4 Conclusions	p. 182
5.5 Problems	p. 182
References	p. 187
6 Introductory Image Processing	p. 189
6.1 Light and Luminance	p. 190
6.2 Still Image Visual Properties	p. 194
6.2.1 Weber's Law	p. 195
6.2.2 Contrast Sensitivity Function	p. 196
6.2.3 Local Contrast Adaptation	p. 198
6.3 Time-Variant Human Visual System Properties	p. 199
6.4 Image Sensors	p. 201
6.4.1 Electronic	p. 201
6.4.2 Film	p. 203
6.5 Image and Video Display	p. 204
6.5.1 Gamma	p. 205
6.6 Simple Image Processing Filters	p. 206
6.6.1 Box Filter	p. 206
6.6.2 Gaussian Filter	p. 207
6.6.3 Prewitt Operator	p. 208
6.6.4 Sobel Operator	p. 208
6.6.5 Laplacian Filter	p. 209
6.7 Conclusions	p. 211
6.8 Problems	p. 211
References	p. 213
7 Image Estimation and Restoration	p. 215
7.1 2-D Random Fields	p. 216
7.1.1 Filtering a 2-D Random Field	p. 218
7.1.2 Autoregressive Random Signal Models	p. 222
7.2 Estimation for Random Fields	p. 224
7.2.1 Infinite Observation Domain	p. 225
7.3 2-D Recursive Estimation	p. 229
7.3.1 1-D Kalman Filter	p. 229
7.3.2 2-D Kalman Filtering	p. 233
7.3.3 Reduced Update Kalman Filter	p. 235
7.3.4 Approximate RUKF	p. 236
7.3.5 Steady-State RUKF	p. 236
7.3.6 LSI Estimation and Restoration Examples with RUKF	p. 237
7.4 Inhomogeneous Gaussian Estimation	p. 241
7.4.1 Inhomogeneous Estimation with RUKF	p. 243
7.5 Estimation in the Subband/Wavelet Domain	p. 244
7.6 Bayesian and MAP Estimation	p. 248
7.6.1 Gauss Markov Image Models	p. 249
7.6.2 Simulated Annealing	p. 253
7.7 Image Identification and Restoration	p. 257
7.7.1 Expectation-Maximization Algorithm Approach	p. 258
7.7.2 EM Method in the Subband/Wavelet Domain	p. 262
7.8 Color Image Processing	p. 263
7.9 Conclusions	p. 263
7.10 Problems	p. 263
References	p. 266
8 Digital Image Compression	p. 269
8.1 Introduction	p. 270
8.2 Transformation	p. 272
8.2.1 DCT	p. 272
8.2.2 SWT	p. 274
8.2.3 DPCM	p. 275
8.3 Quantization	p. 276
8.3.1 Uniform Quantization	p. 278
8.3.2 Optimal MSE Quantization	p. 278
8.3.3 Vector Quantization	p. 280
8.3.4 LBG Algorithm [7]	p. 282
8.4 Entropy Coding	p. 284
8.4.1 Huffman Coding	p. 285
8.4.2 Arithmetic Coding	p. 286
8.4.3 ECSQ and ECVQ	p. 287
8.5 DCT Coder	p. 289
8.6 SWT Coder	p. 292
8.6.1 Multiresolution SWT Coding	p. 298
8.6.2 Nondyadic SWT Decompositions	p. 300
8.6.3 Fully Embedded SWT Coders	p. 300
8.6.4 Embedded Zero-Tree Wavelet (EZW) Coder	p. 301
8.6.5 Set Partitioning in Hierarchical Trees (SPIHT) Coder	p. 304
8.6.6 Embedded Zero Block Coder (EZBC)	p. 306
8.7 JPEG 2000	p. 308
8.8 Color Image Coding	p. 309
8.8.1 Scalable Coder Results Comparison	p. 311
8.9 Robustness Considerations	p. 311
8.10 Conclusions	p. 312
8.11 Problems	p. 312
References	p. 315
9 Three-Dimensional and Spatiotemporal Processing	p. 317
9.1 3-D Signals and Systems	p. 318
9.1.1 Properties of 3-D Fourier Transform	p. 320
9.1.2 3-D Filters	p. 321
9.2 3-D Sampling and Reconstruction	p. 321
9.2.1 General 3-D Sampling	p. 323
9.3 Spatiotemporal Signal Processing	p. 325
9.3.1 Spatiotemporal Sampling	p. 325
9.3.2 Spatiotemporal Filters	p. 326
9.3.3 Intraframe Filtering	p. 328
9.3.4 Intraframe Wiener Filter	p. 328
9.3.5 Interframe Filtering	p. 330
9.3.6 Interframe Wiener Filter	p. 331
9.4 Spatiotemporal Markov Models	p. 332
9.4.1 Causal and Semicausal 3-D Field Sequences	p. 333
9.4.2 Reduced Update Spatiotemporal Kalman Filter	p. 335
9.5 Conclusions	p. 338
9.6 Problems	p. 338
References	p. 339
10 Digital Video Processing	p. 341
10.1 Interframe Processing	p. 342
10.2 Motion Estimation and Motion Compensation	p. 348
10.2.1 Block Matching Method	p. 350
10.2.2 Hierarchical Block Matching	p. 353
10.2.3 Overlapped Block Motion Compensation	p. 354
10.2.4 Pel-Recursive Motion Estimation	p. 355
10.2.5 Optical flow methods	p. 356
10.3 Motion-Compensated Filtering	p. 358
10.3.1 MC-Wiener Filter	p. 358
10.3.2 MC-Kalman Filter	p. 360
10.3.3 Frame-Rate Conversion	p. 363
10.3.4 Deinterlacing	p. 365
10.4 Bayesian Method for Estimating Motion	p. 371
10.4.1 Joint Motion Estimation and Segmentation	p. 373
10.5 Conclusions	p. 377
10.6 Problems	p. 378
References	p. 379
10.7 Appendix: Digital Video Formats	p. 380
SIF	p. 381
CIF	p. 381
ITU 601 Digital TV (aka SMPTE D1 and D5)	p. 381
ATSC Formats	p. 382
11 Digital Video Compression	p. 385
11.1 Intraframe Coding	p. 387
11.1.1 M-JPEG Pseudo Algorithm	p. 388
11.1.2 DV Codec	p. 391
11.1.3 Intraframe SWT Coding	p. 392
11.1.4 M-JPEG 2000	p. 394
11.2 Interframe Coding	p. 395
11.2.1 Generalizing 1-D DPCM to Interframe Coding	p. 396
11.2.2 MC Spatiotemporal Prediction	p. 397
11.3 Interframe Coding Standards	p. 398
11.3.1 MPEG 1	p. 399
11.3.2 MPEG 2-"a Generic Standard"	p. 401
11.3.3 The Missing MPEG 3-High-Definition Television	p. 403
11.3.4 MPEG 4-Natural and Synthetic Combined	p. 403
11.3.5 Video Processing of MPEG-Coded Bitstreams	p. 404
11.3.6 H.263 Coder for Visual Conferencing	p. 405
11.3.7 H.264/AVC	p. 405
11.3.8 Video Coder Mode Control	p. 408
11.3.9 Network Adaptation	p. 410
11.4 Interframe SWT Coders	p. 410
11.4.1 Motion-Compensated SWT Hybrid Coding	p. 412
11.4.2 3-D or Spatiotemporal Transform Coding	p. 413
11.5 Scalable Video Coders	p. 417
11.5.1 More on MCTF	p. 420
11.5.2 Detection of Covered Pixels	p. 421
11.5.3 Bidirectional MCTF	p. 423
11.6 Object-Based Video Coding	p. 426
11.7 Comments on the Sensitivity of Compressed Video	p. 428
11.8 Conclusions	p. 429
11.9 Problems	p. 430
References	p. 431
12 Video Transmission over Networks	p. 435
12.1 Video on IP Networks	p. 436
12.1.1 Overview of IP Networks	p. 437
12.1.2 Error-Resilient Coding	p. 440
12.1.3 Transport-Level Error Control	p. 442
12.1.4 Wireless Networks	p. 443
12.1.5 Joint Source-Channel Coding	p. 444
12.1.6 Error Concealment	p. 446
12.2 Robust SWT Video Coding (Bajic)	p. 447
12.2.1 Dispersive Packetization	p. 447
12.2.2 Multiple Description FEC	p. 453
12.3 Error-Resilience Features of H.264/AVC	p. 458
12.3.1 Syntax	p. 458
12.3.2 Data Partitioning	p. 459
12.3.3 Slice Interleaving and Flexible Macroblock Ordering	p. 459
12.3.4 Switching Frames	p. 459
12.3.5 Reference Frame Selection	p. 461
12.3.6 Intrablock Refreshing	p. 461
12.3.7 Error Concealment in H.264/AVC	p. 461
12.4 Joint Source-Network Coding	p. 463
12.4.1 Digital Item Adaptation (DIA) in MPEG 21	p. 463
12.4.2 Fine-Grain Adaptive FEC	p. 464
12.5 Conclusions	p. 469
12.6 Problems	p. 469
References	p. 471
Index	p. 477

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